1. Field of the Invention
The invention relates to an apparatus and method for adjusting frequency response of a reactive circuit, and, more specifically, to the trimming of a main RC circuit by component selection within the main RC circuit.
2. Description of the Background
Active RC circuits are used in electronics applications known in the art. Such circuits are employed in the design of continuous time analog integrated circuits, such as analog filters and sigma delta converters. In a typical integrated circuit application, resistors and capacitors created as part of the integrated circuit are created within predetermined tolerance levels. The frequency response of these integrated RC circuits depend on the absolute value of the resistors and capacitors, and the tolerances thereof. Typically, an on-chip resistance varies within a tolerance of plus or minus 20% of desired value, and an on chip capacitance may vary, for example, within a tolerance of plus or minus 10%. Therefore, the RC time constant of a given circuit may vary within up to plus or minus 30% tolerance level. Unfortunately, in many applications of RC circuit technology, a variation of plus or minus 30% may be not within acceptable limits.
An RC circuit may be a first order low pass filter with −3 dB bandwidth frequency of 1/(2πRC). In higher order filters, the product of RC defines filter frequency response. The product of resistance and capacitance, tau, may be the time constant of the RC circuit in seconds, where R may be the resistance in Ohms, and C may be the capacitance in Farads of the RC circuit. As may be known to those possessing an ordinary skill in the pertinent art, a capacitor does not charge at a steady rate. Rather, the rate of charge for a capacitor may be rapid at first, and may slow considerably as the capacitor reaches full charge. During each time constant value, tau, the capacitor charges 63.2% of the remaining distance to the maximum voltage charge level. A capacitor may be 99.33 percent charged at the end of five time constant values, and may be charged to 99.9 percent of its final value after 6.9 time constant values.
Similarly, a capacitor does not discharge at a steady rate. Rather, the rate of discharge may be rapid at first, and slows considerably as the charge on the capacitor approaches zero. During each time constant period, the capacitor discharges 63.2% of the remaining distance to the minimum voltage charge level. A capacitor may be 99.33 percent discharged at the end of five time constant values, and may be discharged to 99.9 percent of its final value after 6.9 time constant values.
Thus, variations in the R and C value may cause unacceptably wide variations in the time constant tau, and may lead to improper time estimates for full charging and discharging of a capacitor in an RC circuit. RC filters employ RC circuitry that may be subject to time constant values. A lack of clarity as to the performance, i.e. the charging and discharging of such a filter, may cause unacceptable performance levels in applications employing filtering, particularly in applications wherein higher order filters are employed. For example, the wireless communication industry, and the hardware employed therein, are highly dependent on filtering processes, thus making wide swings in time constant values unacceptable.
Therefore, the need exists for an apparatus and method for improving the tolerance of an RC circuit, such as an RC filtering circuit.